Analysis of charge transport: a mathematical study of semiconductor devices
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1996
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 167 S. |
| ISBN: | 3540603182 |
Staff View
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Record in the Search Index
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| adam_text | JOSEPH W. JEROME ANALYSIS OF CHARGE TRANSPORT A MATHEMATICAL STUDY OF
SEMICONDUCTOR DEVICES SPRINGER TABLE OF CONTENTS PREFACE VII 1.
INTRODUCTION 1 1.1 MODELING 2 1.2 COMPUTATIONAL FOUNDATIONS 3 1.3
MATHEMATICAL THEORY 5 1.4 SUMMARY 5 PART I. MODELING OF SEMICONDUCTOR
DEVICES 2. DEVELOPMENT OF DRIFT-DIFFUSION MODELS 9 2.1 DESCRIPTIVE
BACKGROUND 9 2.2 MODELING OVERVIEW 10 2.3 SCALING AND JUNCTION WIDTH
ESTIMATION 14 2.3.1 SYSTEM AND SCALINGS 14 2.3.2 EXAMPLE AND HEURISTIC
ANALYSIS 17 2.4 THE SCHARFETTER-GUMMEL DISCRETIZATION 19 2.4.1
VARIATIONAL CALCULUS 19 2.4.2 PIECEWISE CONSTANT FLUX 21 2.5 A MODEL FOR
DRIFT-DIFFUSION 23 2.5.1 THE MOBILITY RELATIONS 24 2.5.2 BOUNDARY
CONDITIONS AND CURRENT-VOLTAGE RELATIONS .. 25 3. MOMENT MODELS:
MICROSCOPIC TO MACROSCOPIC 27 3.1 THE HYDRODYNAMIC MODEL 27 3.1.1
CHARGE, MOMENTUM AND ENERGY TRANSPORT EQUATIONS . 27 3.1.2 MOMENT
CLOSURE AND RELAXATION RELATIONS 30 3.2 CALIBRATION WITH THE MECHANICS
OF CHARGED FLUIDS 33 3.2.1 CONSERVATION OF MASS AND ENERGY 33 3.2.2 THE
MOMENTUM SUBSYSTEM 35 3.3 SUBSONIC LINEARIZATION ANALYSIS IN ONE
DIMENSION 36 3.4 ENERGY TRANSPORT MODELS AND STOKES FLOW 39 3.4.1 THE
STEADY-STATE SYSTEM 40 X TABLE OF CONTENTS 3.4.2 EXPONENTIAL VARIABLES
IN ONE DIMENSION 41 3.4.3 MAXIMUM PRINCIPLES 42 3.4.4 THE FIXED POINT
MAP 44 3.5 MODELING ISSUES 45 3.5.1 REGIMES DEFINED BY DAMPING 46 3.6 A
GLIMPSE OF THE QUANTUM HYDRODYNAMIC MODEL 47 PART II. COMPUTATIONAL
FOUNDATIONS 4. A FAMILY OF SOLUTION FIXED POINT MAPS: PARTIAL DECOUPLING
53 4.1 CONTRACTION PROPERTY OF THE GUMMEL MAP IN TWO DIMENSIONS 55 4.1.1
A FRAMEWORK FOR THE GUMMEL MAP 56 4.1.2 THE PRINCIPAL RESULT 57 4.1.3
THE SUPPORTING LEMMAS AND HYPOTHESES 59 4.2 GENERAL CASE: A FRAMEWORK OF
WEIGHTED SPACES 65 4.3 EXISTENCE AND MAXIMUM PRINCIPLES FOR U/ 67 4.4
ADMISSIBLE LAG AND THE MAPPING VW/ 70 4.4.1 ADMISSIBLE LAGGING OF THE
CONTINUITY SUBSYSTEM 71 4.4.2 UNIQUENESS AND DEFINITION OF THE MAP VW/
73 4.5 A VARIATIONAL INEQUALITY FOR THE CURRENT CONTINUITY SUBSYSTEM 74
4.5.1 ABSTRACT INEQUALITY FORMULATION 75 4.5.2 THE CONCRETE VARIATIONAL
INEQUALITY 77 4.6 EQUIVALENCE WITH THE CURRENT CONTINUITY SUBSYSTEM 79
4.7 COMPACTNESS AND CONTINUITY OF VW/ AND FIXED POINTS OF T/ 82 4.7.1
COMPACTNESS 82 4.7.2 CONTINUITY 82 4.7.3 THE GUMMEL MAP AND ITS FIXED
POINTS 84 4.8 TECHNICAL PROPERTIES OF NORMS AND MAPPINGS 84 4.8.1 NORM
EQUIVALENCE 84 4.8.2 ENHANCED CONTINUITY FOR THE SUBSYSTEM MAP 85 5.
NONLINEAR CONVERGENCE THEORY FOR FINITE ELEMENTS 89 5.1 DEFINITIONS OF
THE COMPOSITE MAPPINGS OF T 90 5.2 THE NUMERICAL MAP T N 94 5.2.1 THE
COMPOSITE FINITE ELEMENT MAPS 94 5.2.2 THE DISCRETE MAXIMUM PRINCIPLES
95 5.2.3 THE NUMERICAL FIXED POINT MAP 97 5.3 APPROXIMATION THEORY IN
ENERGY NORMS AND POINTWISE NORMS 98 5.3.1 APPROXIMATION THEORY FOR
GRADIENT EQUATIONS 99 TABLE OF CONTENTS XI 5.3.2 CONVERGENCE PROPERTIES
OF T N IN ENERGY NORMS 103 5.3.3 CONVERGENCE PROPERTIES OF T* IN THE
POINTWISE NORM . 104 5.4 A CALCULUS FOR THE SYSTEM MAPPINGS 105 5.4.1
THE MAP U: DIFFERENTIABILITY PROPERTIES 106 5.4.2 THE MAPPINGS V AND W:
DIFFERENTIABILITY PROPERTIES . 108 5.5 THE MAPPINGS U/,, V^, AND W/J 111
5.5.1 THE MAPPING XJ H 112 5.5.2 THE MAPPINGS V,, AND W A 113 5.6
SUMMARY OF RESULTS FOR T AND T N 117 5.7 VERIFICATION OF THE GENERAL
HYPOTHESES 119 5.7.1 VERIFICATION OF THE A PRIORI ESTIMATES 119 5.7.2
VERIFICATION OF THE A POSTERIORI ESTIMATES 119 5.8 FINAL CONVERGENCE
RESULTS 121 PART III. MATHEMATICAL THEORY 6. NUMERICAL FIXED POINT
APPROXIMATION IN BANACH SPACE . . 125 6.1 LINEAR THEORY: STAIRCASE TO
THE NONLINEAR THEORY 126 6.2 NONLINEAR ESTIMATION AND THE OPERATOR
CALCULUS 128 6.2.1 A PRIORI ESTIMATES AND ASYMPTOTIC LINEARITY 129
6.2.2 A POSTERIORI ESTIMATES 133 6.3 APPROXIMATE FIXED POINTS VIA
NEWTON S METHOD 135 6.4 THE INF-SUP THEORY AS A SPECIAL CASE 140 7.
CONSTRUCTION OF THE DISCRETE APPROXIMATION SEQUENCE .... 143 7.1 THE
FIXED POINT MAP AS SMOOTHER 143 7.1.1 SOLUTION OF THE CENTRAL
APPROXIMATION PROBLEM 145 7.2 SMOOTHING FOR NEWTON ITERATION:
DIFFERENTIAL MAPS 146 7.2.1 FRAMEWORK FOR THE POSTCONDITIONING ITERATION
147 7.2.2 THE SUPERLINEAR CONVERGENCE THEOREM 149 REFERENCES 155 INDEX
163
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| any_adam_object | 1 |
| author | Jerome, Joseph W. |
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| dewey-full | 537.6/225/01175 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 537 - Electricity and electronics |
| dewey-raw | 537.6/225/01175 |
| dewey-search | 537.6/225/01175 |
| dewey-sort | 3537.6 3225 41175 |
| dewey-tens | 530 - Physics |
| discipline | Physik Elektrotechnik Mathematik |
| format | Book |
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| physical | XI, 167 S. |
| publishDate | 1996 |
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| spelling | Jerome, Joseph W. Verfasser aut Analysis of charge transport a mathematical study of semiconductor devices Joseph W. Jerome Berlin [u.a.] Springer 1996 XI, 167 S. txt rdacontent n rdamedia nc rdacarrier Mathematisches Modell Charge transfer Mathematical models Semiconductors Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Halbleiterbauelement (DE-588)4113826-0 gnd rswk-swf Ladungstransport (DE-588)4166400-0 gnd rswk-swf Halbleiterbauelement (DE-588)4113826-0 s Ladungstransport (DE-588)4166400-0 s Mathematisches Modell (DE-588)4114528-8 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006959645&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jerome, Joseph W. Analysis of charge transport a mathematical study of semiconductor devices Mathematisches Modell Charge transfer Mathematical models Semiconductors Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd Halbleiterbauelement (DE-588)4113826-0 gnd Ladungstransport (DE-588)4166400-0 gnd |
| subject_GND | (DE-588)4114528-8 (DE-588)4113826-0 (DE-588)4166400-0 |
| title | Analysis of charge transport a mathematical study of semiconductor devices |
| title_auth | Analysis of charge transport a mathematical study of semiconductor devices |
| title_exact_search | Analysis of charge transport a mathematical study of semiconductor devices |
| title_full | Analysis of charge transport a mathematical study of semiconductor devices Joseph W. Jerome |
| title_fullStr | Analysis of charge transport a mathematical study of semiconductor devices Joseph W. Jerome |
| title_full_unstemmed | Analysis of charge transport a mathematical study of semiconductor devices Joseph W. Jerome |
| title_short | Analysis of charge transport |
| title_sort | analysis of charge transport a mathematical study of semiconductor devices |
| title_sub | a mathematical study of semiconductor devices |
| topic | Mathematisches Modell Charge transfer Mathematical models Semiconductors Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd Halbleiterbauelement (DE-588)4113826-0 gnd Ladungstransport (DE-588)4166400-0 gnd |
| topic_facet | Mathematisches Modell Charge transfer Mathematical models Semiconductors Mathematical models Halbleiterbauelement Ladungstransport |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006959645&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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